Master Thesis

P-release kinetic as a predictor for P-availability in the STYCS Trials

Marc Jerónimo Pérez y Ropero

Introduction

In my Internship I studied the current GRUD, particularly Mg, P and K
Fertilizer requirement models imply \(Y\sim STP + Clay\) & \(P-\text{Export}\sim STP + Clay\)
Currently only stationary measurement of STP are considered
Could a kinetic desorption-model better explain the soil status and yield data?

LTE STYCS, all treatment conditions equal except P-fertilization, which is in 6 Levels, 3 were considered(\(P0\),\(P100\),\(P166\))
4 Sites regarded; Ellighausen, Rümlang-Altwi, Oensingen, Zürich-Reckenholz
5 Sites, 4 blocks per site, 6 Treatment-Levels, 4 Repetitions
Years 2017-2022 were modelled, kinetic data was collected only for year 2022

The net-desorption was modeled using a first-order kinetic equation:

1. The Rate of Release: The change in P over time is proportional to the remaining desorbable P. \[\frac{dP}{dt}=k \times (P^S-P)\]

2. The Solution: When solved, this gives us the equation for the curve: \[P(t)=P^S \times (1-e^{-kt})\]

Relevant Variables

Soil Variables:

\(P-CO_2\) & \(P-AAE10\) stand for the GRUD STP-measurements in [\(g~P/kg ~ Soil\)]
\(k\)(\(s^{-1}\)) can be interpreted as the relative speed of net-desorption of orthophosphate
\(k*PS\)(\(g~Ps^{-1}\)) can be interpreted as the average net-release speed
\(PS\)(\(mg~P/L~H_2O\)) is the equilibrium concentration of \(PO_4^{3-}\) of the net-desorption experiment
From the 0-20cm Horizon: Clay-, Silt-,\(C_{org}\)-content and pH

Yield Variables:

For a year \(X\) and crop \(C\) \(Y_{main-rel}\) stands for \(Y_{main-rel}:=Y_C^{X}/mean(Y_C~\text{in year}~X~\text{in CH})\)
For every year:site:crop combination the yield was normalised using: \(Y_\text{norm}:=Y/median(Y_{P166})\)
The P-Export was calculated as the P-Uptake of the main product
The P-Balance was calculated as the difference \(P_{Fertilized}-\text{P-Export}\)

I: Is the method presented by Flossmann and Richter (1982) with the double extraction replicable with the soils from the STYCS-trial?
II: How do GRUD-measurements of STP correlate to the soil properties \(C_\text{org}\)-content, clay-content, silt-content and pH?
III: Are the kinetic coefficients \(k\) and \(PS\) correlated to soil properties?
IV: How well can current GRUD methods of STP (\(P-CO_2\) & \(P-AAE10\)) predict the Yield-parameters, P-Export and P-Balance?
V: How well can the kinetic parameters \(k\) & \(PS\) predict Yield-parameters, P-Export and P-Balance?

The following random structure was chosen:

(1|year) + (1|Site) + (1|Site:block) + (Treatment|Site)

Coefficient Table for Soil Covariates. Significant codes: 0 '***' 0.001 '**' 0.01 '*' 0.05
Predictor	PS	k	log(k*PS)	CO2	AAE10
(Intercept)	-1.772	-0.425	0.039	-0.536	-0.532
Alox		-0.660	-1.204	-0.034	-0.319
Feox		0.020	-0.571	-0.164	-0.138
soil_0_20_clay	1.798	-1.733**	0.611	-0.007	-0.121
soil_0_20_Corg		1.044**	-0.412	0.166	0.232
soil_0_20_pH_H2O	0.000	-0.280	0.094	0.075	0.057
soil_0_20_silt		0.252	0.113	-0.084	0.012
R2m	1.000	0.204	0.224	0.125	0.280
R2c	1.000	0.963	0.976	0.724	0.832

Observation

P-CO2 and P-AAE10 did not correlate with clay-content
k does not correlate with Treatment but with pH and silt-content
\(k*log(PS)\) had significant effects for clay- and silt-content as well as pH, but lower in Treatment
PS was the covariate best predicted by soil properties: \(R^2_m=0.858\)

Coefficient Table for Yield Variables. Significant codes: 0 '***' 0.001 '**' 0.01 '*' 0.05
Predictor	Yn-STP-CO2	Yn-STP-AAE10	Yn-STP-GRUD	Yn-Kinetic	Yr-STP-CO2	Yr-STP-AAE10	Yr-STP-GRUD	Yr-Kinetic
(Intercept)	0.012	0.007	-0.109	0.156	-0.323	-0.257	-0.306	-0.119
k				0.166				-0.018
k:log(PS)				-0.012				0.016
log(PS)				0.066				0.010
log(soil_0_20_P_AAE10)		0.067*	0.432**			0.037	0.046
log(soil_0_20_P_CO2)	0.027		-0.128		-0.001		-0.040
log(soil_0_20_P_CO2):log(soil_0_20_P_AAE10)			0.149*				-0.021
R2m	0.012	0.084	0.291	0.019	0.000	0.011	0.020	0.002
R2c	0.083	0.361	0.436	0.045	0.618	0.698	0.696	0.807

Observation

\(k*log(PS)\) and \(k\) showed the strongest effects in the prediction of Ynorm and Yrel
P-AAE10 did show a significant effect in prediction of Yrel

Coefficient Table for P-export. Significant codes: 0 '***' 0.001 '**' 0.01 '*' 0.05
Predictor	CO2_Pexport	AAE10_Pexport	Grud_Pexport	Kin_Pexport
(Intercept)	0.012	-0.002	0.119	0.596
k				-0.014
k:log(PS)				0.080
log(PS)				-0.018
log(soil_0_20_P_AAE10)		0.025	-0.015
log(soil_0_20_P_CO2)	0.087		0.131
log(soil_0_20_P_CO2):log(soil_0_20_P_AAE10)			0.011
R2m	0.012	0.001	0.016	0.004
R2c	0.654	0.685	0.796	0.789

Observations

Coefficient Table for P-balance. Significant codes: 0 '***' 0.001 '**' 0.01 '*' 0.05
Predictor	CO2_Pbalance	AAE10_Pbalance	Grud_Pbalance	Kin_Pbalance
(Intercept)	0.569*	0.315	0.610*	1.086*
k				0.155
k:log(PS)				-0.151
log(PS)				0.341***
log(soil_0_20_P_AAE10)		0.009	0.009
log(soil_0_20_P_CO2)	-0.023		-0.029
log(soil_0_20_P_CO2):log(soil_0_20_P_AAE10)			0.030
R2m	0.001	0.000	0.006	0.122
R2c	0.590	0.762	0.596	0.699

Observation

\(PS\) showed the strongest effect in predicting P_balance and k showed substantial \(R^2_m\)

The net-desorption of P probably follows a first-order-kinetic, but \(PS\) is difficult to directly estimate.
The kinetic parameters \(k\) and \(PS\) could comparably and sometimes better explain Ynorm, Yrel and P-Balance.
Regarding the difference between \(R^2_m\) and \(R^2_C\) confounded effects seem to be buried in the sites.
P-CO2 and P-AAE10 are not as well explainable as \(PS\) and \(k\), in particular not by clay-content.
P-CO2 correlated however significantly with P-Export

Thank you for your attention